1. Field of the Invention
The present invention relates to seismic data processing and more particularly, to wavelet extraction and deconvolution during seismic data processing.
2. Description of the Related Art
Reflection seismology is a process which records as seismic data for analysis the reflected energy resulting from acoustic impedance changes in the earth due to the location and presence of subsurface formations or structure of interest. The reflected energy results from the transmission of short duration acoustic waves into the earth at locations of interest in a format which is known as a wavelet. The responses to the wavelet were in effect a combined product or convolution of the wavelet and the vertical reflectivity of the earth. To increase the resolution of the data and provide for enhanced ability in its interpretation, it has been common practice to subject the data to a processing technique known as deconvolution. Deconvolution involved removal of the effects of the wavelet on the recorded data.
For several reasons, the actual nature and characteristics of the actual wavelet sent into the earth were not precisely determinable. Two approaches have been used in attempt to take this into account. The first approach has been to assume that the wavelet was of an ideal form known as a zero phase or minimum phase wavelet. In seismic processing, if only seismic data exists, in order to obtain wavelet and proceed deconvolution, routinely a zero phase or minimum phase is assumed followed by inverting the wavelet and applying deconvolution. The conventional wavelet extraction and deconvolution requires zero or minimum phase assumption with two steps of procedure in frequency domain. But in fact the real wavelet is neither zero nor minimum phase.
The second approach was known as blind deconvolution, where a statistical estimate of the form of the wavelet was postulated, based on experience, field data and the like. Various forms of blind deconvolution have been proposed, one of which used what is known as the Markov Chain Monte Carlo (or MCMC) method. Recently, the MCMC method has gained attention in research to address higher order statistics features and thus obtain the wavelet with phase and reflectivity simultaneously. However, the MCMC method as a blind solution for simultaneous wavelet estimation and deconvolution has ambiguity problems, as well as other practical limitations which prevent the algorithm from being practically applied in seismic processing. The Markov Chain Monte Carlo approach appears to solve both wavelet and deconvolution at the same time. However, challenges prevent the algorithm to be practically applied to seismic industry. The first is that a maximum energy position is required, but such a position is usually unknown. Second, the extracted wavelet has possessed frequencies which were mostly out of the seismic input frequency band. Third, the deconvolution outcome resulting from trace to trace operation sometimes has broken and weakened the seismic events since multiple wavelets are extracted from multi-channel traces.
Blind deconvolution using the MCMC approach has thus been a research topic in recent years. Unlike traditional power spectrum approaches in the frequency domain done in wavelet extraction and deconvolution, the MCMC approach has treated the deconvolution processing as a problem of parameter estimation to model the reflectivity, wavelet and noise with different statics distributions by multiple sampling in the time domain. After adequate iterations of sampling, the wavelet and reflectivity series have been intended to converge to the real geological model.
The MCMC approach to blind deconvolution has, so far as is known, made certain assumptions prior to parameter estimations and then applied what is known as a Bayes approach for the implementation. The reflectivity sequence has been assumed to be random (white noise) and susceptible to being modeled statistically by what is known as a Bernoulli-Gaussian process. Another assumption has been that the wavelet can be represented by a multivariate Gaussian function. A further assumption has been that any noise present is uncorrelated, and therefore can be modeled by an independent identically distributed Gaussian function with mean zero, i.e. Inversed Gamma, distribution.